How to solve this equation:$\Phi(x,y,z)=x+\int_{\Omega(x,y,z)}\Phi(u,v,w)dudvdw$?

Question

Assume that $\Omega(x,y,z)=[0,x]\times[0,y]\times[0,z]\subset \mathbb R^3 ,0\leq x,y,z\leq 1$. Consider equation $$\Phi(x,y,z)=x+\int_{\Omega(x,y,z)}\Phi(u,v,w)dudvdw$$The question is: is there any Riemann integrable solution of this equation. I found this question on a test paper in the calculus curriculum, and this is way beyond my ability, so I wonder what kind of methods should we use to solve it.